Journal of Nonlinear Mathematical Physics

Volume 7, Issue 1, February 2000, Pages 1 - 13

Lax Pairs, Painlevé Properties and Exact Solutions of the Calogero Korteweg-de Vries Equation and a New (2 + 1)-Dimensional Equation

Authors
Song-Ju YU, Kouichi TODA
Corresponding Author
Song-Ju YU
Received 4 May 1999, Revised 13 June 1999, Accepted 14 July 1999, Available Online 1 February 2000.
DOI
https://doi.org/10.2991/jnmp.2000.7.1.1How to use a DOI?
Abstract
We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2 + 1)-dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)-dimensional CKdV equation. We show that the CKdV equation as well as the (2+1)-dimensional CKdV equation are integrable in the sense that they possess the Painlevé property. Some exact solutions are also constructed.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
7 - 1
Pages
1 - 13
Publication Date
2000/02
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2000.7.1.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Song-Ju YU
AU  - Kouichi TODA
PY  - 2000
DA  - 2000/02
TI  - Lax Pairs, Painlevé Properties and Exact Solutions of the Calogero Korteweg-de Vries Equation and a New (2 + 1)-Dimensional Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 13
VL  - 7
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2000.7.1.1
DO  - https://doi.org/10.2991/jnmp.2000.7.1.1
ID  - YU2000
ER  -